Parallel Newton-Krylov Method for Rotary-Wing Flowfield Calculations

A Parallel Inexact Newton Method Using A Krylov Multisplitting Algorithm

Scalable Parallel Newton-Krylov Solvers for Discontinuous Galerkin Discretizations

We present techniques for implicit solution of discontinuous Galerkin discretizations of the Navier-Stokes equations on parallel computers. While a block-Jacobi method is simple and straight-forward to parallelize, its convergence properties are poor except for simple problems. Therefore, we consider Newton-GMRES methods preconditioned with block-incomplete LU factorizations, with optimized ele...

Short Communication A Parallel Newton–Krylov Method for Navier–Stokes Rotorcraft Codes

The application of Krylov subspace iterative methods to unsteady three-dimensional Navier–Stokes codes on massively parallel and distributed computing environments is investigated. Previously, the Euler mode of the Navier–Stokes flow solver Transonic Unsteady Rotor Navier–Stokes (TURNS) has been coupled with a Newton–Krylov scheme which uses two Conjugate-Gradient-like (CG) iterative methods. F...

Parallel Two-Grid Semismooth Newton-Krylov-Schwarz Method for Nonlinear Complementarity Problems

We develop scalable parallel domain decomposition algorithms for nonlinear complementarity problems including, for example, obstacle problems and free boundary value problems. Semismooth Newton is a popular approach for such problems, however, the method is not suitable for large scale calculations because the number of Newton iterations is not scalable with respect to the grid size; i.e., when...

A parallel Newton-Krylov method for optimal control of the monodomain model in cardiac electrophysiology

This work addresses an optimal control approach for a model problem in cardiac electrophysiology. A rather complete treatment including the analysis of the model equations, derivation of the optimality system, description of its discretization and a numerical feasibility study in a parallel environment is provided.